With his wildly differing styles and notorious reluctance to be interviewed, the German painter Gerhard Richter is one of the most enigmatic of artists. Yet Martin Gayford finds him surprisingly talkative about his history, painting, and his forthcoming series of exhibitions

At 76, Gerhard Richter is among the most renowned artists in the world. Along with Lucian Freud and Jasper Johns, he is frequently mentioned in lists of candidates for the title of 'greatest living painter'. For the past couple of decades he has been ubiquitous in the art world as a presence and an influence. As much as anyone, he managed to give painting currency in an avant-garde art world dominated by video, conceptual, performance and installation art. A lot of contemporary painting - the Belgian Luc Tuymans's photo-based work, Damien Hirst's spot paintings - is visibly derived from Richter.

His personal history, involving a searing encounter with Nazism and defection from Communist East Germany, could scarcely be more sensational. Yet Richter remains, both as a man and an artist, enigmatic (an adjective used by almost everyone writing about him).

Most famous artists have a signature style. But Richter's work is bewilderingly various. Glenn Lowry, the director of the Museum of Modern Art, New York - which six years ago mounted a massive retrospective of his work - noted that 'Richter is the author of pictures so different from one another that at first glance they seem to be by different hands.' Some are photo-realist, some messily abstract, some cleanly geometric. He himself rarely grants interviews. When asked to make a statement at the press conference of his New York exhibition, he simply shook his head.

Soon British audiences will have an opportunity to contemplate Richter's work in a multiplicity of modes. This autumn there is an exhibition of his geometric abstract paintings at the Serpentine Gallery in London, while a room at Tate Modern is filled with his six Cage Paintings (a completely different variety of abstraction) named after the American composer John Cage, who once proclaimed, 'I have nothing to say and I'm saying it' - a statement that Richter has echoed and obviously approves of. Later in the season another big show of his work - both figurative and abstract - opens in Edinburgh. Next spring yet another exhibition, of his portraits, comes to the National Portrait Gallery, London.

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When I met him in his office-cum-studio space in central Cologne, Richter turned out to be far less taciturn than his reputation suggested. In person he is small, neatly dressed, self-deprecating and wry. It is hard to imagine anyone who behaves less like a famous artist, especially a cool avant-garde one.

'I am,' he tells me happily, 'ridiculously old-fashioned.' He disapproves of the way his children's teachers dress in jeans, 'as if they were going to a picnic' (he has a teenage family by his third wife, Sabine). And he dislikes the irony and humour of much contemporary art. 'To me, it's mainly entertainment. Art should be serious, not a joke. I don't like to laugh about art.'

On the other hand, he is playfully ironic about other questions. 'Why do people listen to Wagner?' he suddenly inquired. 'I just don't understand it.' Then he laughed. Personally, Richter went on, he is allergic to the sound of Tristan and Götterdämmerung. That morning he had been listening to a piece much more to his taste, by the minimalist American composer Steve Reich.

Richter is a very un-Wagnerian artist and personality, even though his biography contains elements of drama and tragedy. He was born in 1932, and lived during his early years in small villages outside Dresden. As a 13-year-old, he saw the glow of the firestorm on the horizon.

When he was studying art after the war, he did so in a city the centre of which was composed of blackened rubble. He and his fellow students spent part of their time each week clearing debris. In another, ideological and intellectual sense, Richter came of age in a burnt-out zone.

The relations of his immediate family with contemporary history were nothing short of horrific. His father, Horst, a schoolteacher, joined the Nazi party. His mother's brother, Rudi, joined the army and was killed shortly afterwards. Her younger sister, Marianne, a schizophrenic, was sent to a mental institution, forcibly sterilised, then later starved to death in a euthanasia camp - part of a Nazi programme to exterminate the mentally ill.

Marianne features in a painting of the same name, from 1965. Like Richter's other figurative paintings it is taken from a photograph - in this case a family snap of her, a shy teenage girl, proudly holding her baby nephew, the four-month-old Gerhard Richter. It is a glimpse of a moment of happiness, seen through a black chasm of history.

At the time when he painted the picture, though he knew Marianne's fate was terrible, he did not know the full details. The final twist emerged only a few years ago, dug up by an investigative author. It seems that the father of Richter's first wife, Heinrich Eufinger, was the doctor responsible for the sterilisation and euthanasia of the mentally ill. The painting itself sold two years ago at auction for £2.1million.

Richter's vocation as a painter and his need to survive this cataclysm of mid-20th-century Germany seem linked in his mind. I asked him why he believed so strongly in this venerable - indeed, prehistoric - medium. His answer was characteristically downbeat. 'I believe in painting and I believe in eating too. What can we do? We have to eat, we have to paint, we have to live. Of course, there are different ways to survive. But it's my best option. I didn't have so much choice when I was young.'

Did he feel, studying in the debris of Dresden, as if he was beginning from zero, a tabula rasa? 'No, I was conscious of a great tradition, even when there were more ruins than houses, the tradition was there.' The cultural inheritance of painting - and the other arts of music, architecture and literature - is something Richter absorbed from his mother, a concert pianist.

In some notes he jotted down in 1964, when he was 32, he remarked, 'In every respect, my work has more to do with traditional art than with anything else.' He would like to paint like Vermeer of Delft - with that precision and detailed clarity - he told the American critic and curator Robert Storr, but he can't. The comparison with Vermeer is an interesting one.

The Dutch master is often believed to have used pre-photographic equipment, such as the camera obscura, just as Richter uses photographs as the basis for his figurative paintings. There is a gloomy, 17th-century side to Richter's subject matter. Among his subjects are candles and skulls - time-honoured symbols of mortality. One category of his work on the website gerhard-richter.com - including Aunt Marianne and Uncle Rudi - is simply labelled 'Death'.

Like Vermeer, Richter is clear and precise. Painters divide into two groups: ones with tidy studios, and others with messy work environments. The New York Times critic, Michael Kimmelman, inspecting Richter's studio floor, found only a single speck of spilt paint - this despite the fact that the majority of his works are large, thickly painted abstracts. Richter's routine is similarly regular. He rises early, paints, lunches (always hummus, tomatoes and yogurt), then works again for a couple of hours in the afternoon.

He no longer works in the ex-factory space where we met, but in a house-cum-studio he designed himself on the outskirts of the city (he is fascinated by architecture). It turns a blank concrete wall to the world. Some years ago the neighbours complained of its grimness, so he planted some trees along it to mitigate its sternness.

Like most major artists, Richter is an obsessive worker. At that moment, though, he complained, 'I have too many shows taking place at the same time, and it's making much more work. That takes all my energy and I can't find time to paint.'

If possible, he likes to work on pictures in series, half a dozen at a time. 'That way,' he said, 'they learn from each other.' The best example was the Cage Paintings three years ago, which are on show at Tate Modern now. 'That was a very good summer; three months and six large paintings.' Richter - Nicholas Serota will be pleased to note - is a fan of Tate Modern, 'the most interesting museum I know, even though I hate many things there.'

Just as his workload and success make it difficult to attain the order he would like in his life, the pictures themselves seem to resist the close-focus precision he aspires to. As he explained to Storr, almost always (though not in the case of Lesende, [The Reader] of 1994 - a portrait of his wife Sabine) he has to blur the image in order to make the picture work. 'It's an emergency move at the end. To make the picture attractive to look at.'

His abstracts are also often produced by a process of systematic smearing and what he calls 'mechanical sweeping', with a sort of home-made squeegee - a technique that, as with a lot of his work, allows some scope for chance. They start out as hard-edged geometrical forms and end up as a shimmering surface that looks as if it might be an image of something - light on water, perhaps.

Richter's different ways of working are all ways of painting while making the minimal claim to any special moral, imaginative or spiritual authority. The abstracts may have a lot of the allure of, say, a late Monet, while remaining just layers of squeezed and smoothed-over paint. The photo-realist works - drawn from an enormous photographic image-bank-cum-archive that he calls Atlas - just look like paintings of photographs.

Many people find them cool, even chilly. But Richter himself thinks them the reverse: that they are embarrassingly hot and crammed with private emotions. 'I feel they are shameless, they so directly reflect what I am thinking and feeling.' And surely he is right. Some of them, such as Aunt Marianne, and the smiling Uncle Rudi are almost radioactive with toxic history. On the other hand, the beautiful Lesende is quite openly full of love. The same is true of Ema (Nude on a Staircase) (1966) a picture of his first wife nude, walking downstairs, that is in the collection of the Ludwig Museum in Cologne (this will be in the National Portrait Gallery show).

After the war, when he was studying art, he was doing so in Communist East Germany, where modernism and 'formalism' were officially disapproved. His first works - though he does not regard them as part of his true opus as an artist - included a mural in the Dresden Museum of Hygiene, Joy of Life. It wasn't until 1959 that he saw the stars of post-war art such as Jackson Pollock and the Italian Lucio Fontana at Documenta II in Kassel. Three years later he fled to the West, taking just Ema with him. He never saw his parents again.

He then started anew, studying at the Art Academy in Dusseldorf, which was dominated in those years by Joseph Beuys, Richter's predecessor as the most celebrated living German artist, and a completely opposite personality. Beuys was everything Richter is not - a performer, an extrovert, a media figure who always appeared wearing a sort of uniform including a hat and jeans and once spent a week in a cage trying to communicate with a coyote for artistic reasons. 'I was always a little sceptical about Beuys,' Richter recalled.

What he misses about the old days is artistic controversy. There is, he said, not nearly enough conflict in the artistic world. 'Occasionally someone will attack Richter, for example, but it's inconsequential.' In the past there was ferocious criticism among Richter and his circle - which included Sigmar Polke and Richter's second wife, Isa Genzken (now a highly fashionable artist herself). Richter believes in good and bad in art; it is another of the old-fashioned things about him.

He carried on painting through the 1960s and 1970s, although painting was then out of style. His success came in the 1980s - by which time he was already in his fifties. He finds the stratospheric prices now commanded by contemporary art, including his own, distasteful. 'Maybe it was always like this, so crazy and so corrupt, almost criminal. I'm not a historian. It's a sickness, a fever.'

Not surprisingly, Richter emerged from his upbringing with an antipathy to ideology of all kinds. But ideology and history are hard to escape, especially if you are German. The ghosts of the past rose up again last year, over the unlikely subject of a stained-glass window in Cologne Cathedral. Richter had been asked by the architect to make a design for the Gothic south transept. The initial idea was for him to produce representations of 20th-century martyrs killed by the Nazis.

He accepted the commission, but he couldn't make it work. He was playing around one day with a reproduction of one of his abstract paintings of coloured squares when he dropped a template of the window over the abstraction and thought, 'My God! That's it!' He told the cathedral staff that this was the only kind of window he could make. 'We talked about it again and again then finally they said - OK, we'll do it. It was brave of them.'

The bravery was that there is no obvious devotional content in the image at all. In fact, the whole arrangement - like the associated series of paintings, 4900 Colours - is controlled by chance. This strand of Richter's work, originally based on the colour chart of a manufacturer of printer's ink, is ordered according to a sort of mathematic lottery.

'What interests me most about these works is that chance does it better that I can, but I have to prepare the conditions to allow randomness to do its work.' That is, he decides on the scale, and the proportions and the colours to be used. Then chance takes over. But, Richter pointed out, 'Chance determines our lives in important ways. If he hadn't met her, what would have happened to them both?' Life, down to the assortment of genes in our DNA code, is all a matter of chance.

In the original piece, 4096 Colours (1974), 1024 hues and tones each appear four times. For the window, he chose 72 shades that were compatible with the existing stained glass in the cathedral, then 11,500 hand-blown glass panels were made and put together in accordance with a randomising computer program in which each colour is assigned a number. The panels are arranged exactly as the numbers emerge. Richter interfered only once - when a figure '1' was accidentally created. He removed it to make it look more random.

No sooner was it was installed than it started a row. The Archbishop of Cologne, Cardinal Joachim Meisner, did not like it and said so. He told a newspaper that it 'belongs equally in a mosque or another house of prayer', adding that 'if we are going to have a new window, then it should be one that reflects our faith, not just any faith.' Shortly afterwards, without referring to Richter's window directly, the cardinal said that when culture is cut off from God it becomes 'degenerate', and that really stirred things up, because 'degenerate' - in German, entartete - was the word used by the Nazis to describe modern art.

The cardinal was angry, Richter reflects, because his window is not a Catholic window. But the interesting thing is that it looks entirely in place in its grand ecclesiastical setting. The glass may be entirely contemporary, even high-tech - one frequent comparison is with pixels - but there has been glittering light and colour in Christian churches since the days of Chartres and Byzantium. Without making any statement about anything, affirming any belief, or ceasing to be entirely modern, Richter's stained glass fits into that tradition.

It is entirely characteristic of its creator. So too is that, as we leave for lunch, he pauses to help the photographer dismantle her equipment and carry it downstairs. Richter is obviously that unexpected thing in a contemporary art star: a bit of a gent.